A persons Body Mass Index is IWH2 where W is the body weight

A person\'s Body Mass Index is I=W/H^2 where W is the body weight (in kilograms) and H is the body height (in meters). A boy has weight W = 30 kg and height H = 1.3 m. Use the linear approximation to estimate the change in I if   (W, H)  changes to (31, 1.38). (Round your answer to four decimal places.)

  

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A parson\'s Body A person\'s Body Mass ndex s (31, 1.38). Round your answer to four decimal places. Use linear approximation (formula ) , where w is the body weight (in kllograms) and H ls the body helght( dy helght (In meters) A boy has weight W-30 kg and helght H-1.3 m. Use the linear approximation to estimate the change in lif (W·H) changes to meters). A boy on (formul

Solution

f (W,H) = W/H²

f_W = 1/H²

f_H = -2W/H³

f (30,1.3) = 30/1.3² = 17.75

f_W (30,1.3) = 0.59

f_H (30,1.3) = -2*30/1.3³ = -54.62

f (31,1.38) = f (30,1.3) + (31-30)* f_W (30,1.3) + (1.38-1.3) f_H (30,1.3)

= 17.75 + 1 * 0.59 + 0.08 * -54.626

= 13.97